Which of the following are not state functions?
(i) q+ w
(ii) q
(iii) w
(iv) H-TS

Options

A. (II) and(III)
B. (I) and(IV)
C. (II) , (III) and(IV)
D. (I), (II) and(III)

Answer

To determine which of the given options are not state functions, we need to understand the difference between state functions and path functions in thermodynamics.

### Step-by-Step Solution:

1. **Understanding State Functions vs. Path Functions**:
- State functions depend only on the initial and final states of a system. Examples include internal energy (U), enthalpy (H), and entropy (S).
- Path functions depend on the specific path taken to reach from the initial state to the final state. Examples include heat (q) and work (w).

2. **Analyzing Each Option**:
- **(i) q + w**:
- According to the first law of thermodynamics, the change in internal energy (ΔU) is given by ΔU = q + w. Since internal energy is a state function, q + w is related to a state function but is not itself a state function. Therefore, **this is not a state function**.

- **(ii) q**:
- Heat (q) is a path function because it depends on how the energy is transferred (e.g., via heating or work). Therefore, **this is not a state function**.

- **(iii) w**:
- Work (w) is also a path function, as it depends on the process taken to do the work. Therefore, **this is not a state function**.

- **(iv) H - TS**:
- The expression H - TS represents the Gibbs free energy (G). Gibbs free energy is a state function because it depends only on the initial and final states of the system. Therefore, **this is a state function**.

3. **Conclusion**:
- The options that are not state functions are:
- (i) q + w
- (ii) q
- (iii) w

### Final Answer:
The following are not state functions:
- (i) q + w
- (ii) q
- (iii) w